This algorithm was validated for systems of particles in three dimensions, both with and without the presence of a charge [1]}.
When charge is present, it is convenient to split the problem in two subproblems, one for with the same charge, with pair correlation \(g_\mathrm {same}(r)\)  and pair interaction \(V_\mathrm {same}(r)\) , and one for particles with opposite charge, with \(g_\mathrm {opp}(r)\)  and \(V_\mathrm {opp}(r)\) .
Since topological charge is relevant for the spatial distribution of phase singularities in random waves, and it is known that \(g_\mathrm {same}(r) \ne g_\mathrm {opp}(r)\)  [2]}, we here make this distinction.
